Nonlinear optimal control for the five-axle and three-steering coupled-vehicle system

Abstract

Transportation of heavy loads is often performed by multi-axle multi-steered heavy duty vehicles In this article a novel nonlinear optimal control method is applied to the kinematic model of the five-axle and three-steering coupled vehicle system. First, it is proven that the dynamic model of this articulated multi-vehicle system is differentially flat. Next. the state-space model of the five-axle and three-steering vehicle system undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the five-axle and three-steering vehicle system a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and minimal dispersion of energy by the propulsion and steering system of the five-axle and three-steering vehicle system.